The Democratic-controlled House handed President Reagan another budget victory yesterday as it voted, 220 to 207, for a Republican-drafted tax and spending plan for next year that would slash deeply into social welfare spending to keep the projected deficit under $100 billion.

But it was less of a smashing win than Reagan scored in last year's budget battle, coming only after his own original budget was brushed aside and an earlier Republican proposals got washed out in a first round of House budget skirmishing two weeks ago.

Approval of the Republican budget followed defeat, by a vote of 225 to 202, of a Democratic-drafted alternative that aimed to cut domestic spending less and military spending more while raising more in taxes--yet still ended up with a higher deficit: $107.5 billion in contrast with $99.3 billion for the Republican version.

Many Democrats went into the battle resigned to defeat, taking consolation in advance that a Reagan budget victory would make it easier to campaign against "Reagan's economy" in this fall's congressional elections. While supporting their own budget, Democratic leaders did not lobby against the Republican budget, thereby shielding themselves from White House charges of Democratic responsibility if both budgets went down to defeat.

The Republican-controlled Senate last month passed a somewhat less conservative version of the budget, and conferees from the two houses are expected to meet Monday or Tuesday to work out a compromise.

With the Senate's budget projecting a deficit of $116 billion, a deficit of more than $100 billion is virtually assured for next year, despite House Republicans' efforts to keep it under that amount.

House Budget Committee Chairman James R. Jones (D-Okla.), floor leader for the defeated Democratic budget, predicted a difficult conference and said legislation to implement the spending cuts and tax increases would also be difficult to achieve--a point that some Republicans were also suggesting privately.

More than three dozen conservative Democrats joined most Republicans in rejecting the Democratic budget and approving the Republican one, restoring the old GOP-"Boll Weevil" coalition that handed Reagan his big budget victories last year.

Only three Republicans voted for the Democratic budget, while 39 Democrats voted against it. On the Republican plan, 46 Democrats voted yes, while 15 Republicans, mostly moderate "Gypsy Moths," voted no. Among Washington-area House members, only Reps. Michael D. Barnes (D-Md.) and Steny H. Hoyer (D-Md.) voted for the Democratic budget and against the Republican budget.

The Republican alternative was helped along, at least in part, by dire predictions that failure to adopt a budget on this second try might mean no budget at all for fiscal 1983--or what Minority Whip Trent Lott (R-Miss.) warned would be "chaos and confrontation for the rest of the year."

The House Republican plan calls for legislative committees to come up with $8.1 billion in spending cuts and $21 billion in tax increases by July 20.

In all, it sets targets for about $18 billion in domestic spending cuts and $7.9 billion in defense cutbacks, along with other economies that include an increase of no more than 4 percent next year in federal workers' pay and pensions and a 2 percent reduction in the federal work force over the next three years.

In attempting to put together a winnable package after defeat of their first budget two weeks ago, the Republicans made their heaviest cuts in programs for the poor, including welfare, Medicaid, food stamps and other feeding programs.

Shortly after the vote, House Minority Leader Robert H. Michel (R-Ill.) and other party leaders reached Reagan by telephone in Europe. He spoke from a castle on the Rhine, they from a telephone booth in the press gallery where they were holding a news conference.

"We pulled it off. It was a very nice win," Michel told Reagan, who, in a phone call to Michel earlier in the day, had said he would "hold my breath until I'm blue in the face" waiting for the budget to pass. "I hope you didn't have to go to that extreme," Michel told Reagan during the second phone call.

Actually, aides said in Germany that Reagan called only six House members yesterday--three Boll Weevils and three Gypsy Moths. Vice President Bush also met with some wavering moderate Republicans.

Reagan, Michel relayed to reporters, thanked his congressional lieutenants and said he would "sleep a lot better tonight," knowing that the budget he had previously endorsed as "the best available alternative" had finally passed. "Sorry we took so long to get it right," Lott told Reagan.

As to the coming conference, Reagan aide Richard Darman said in Germany, "We can get what we want out of that."

In debate on the two budgets, few members spoke of the choices in glowing terms, reflecting the frustrations arising out of compromises that had to be made to come up with a budget with a deficit close to $100 billion--"five months of idiotic posturing," Rep. Ed Bethune (R-Ark.) called it.

Rep. W.G. Hefner (D-N.C.) spoke for some of the moderate Republicans and Democrats who wound up voting for the Republican budget as preferable to more budget chaos, saying he would "hold my nose a little" in voting for the Democratic budget and then "hold my nose a lot" and vote for the Republican budget.

Some members of the Congressional Black Caucus, who had opposed all the earlier budgets, decided to go along with the Democratic budget this time, although they drew the line against the Republican version.

Just as domestic programs had been squeezed in the Republican budget, the Democrats had fattened their alternative with money for jobs and other traditional party programs to win support of blacks and other liberals who had opposed their previous budget as too conservative.

This still was not enough to make a difference, although an aide to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) noted that the Democrats, even in their defeat yesterday, had scored their highest vote on a budget since Reagan took office.

The Democrats picked up 31 votes from their last total two weeks ago. The Republicans picked up 28.

Passage of the Republican alternative spared the House from having to vote on Reagan's own budget, which was waiting to be taken up if both others failed. Largely because of its projected deficit of $122 billion, many Republicans wanted to be spared the pain of having to vote on it. After voting on the two alternatives, the House officially passed the budget by a vote of 219 to 206.